The Matildas, who face the U.S. women's team Wednesday in Cary, N.C., in the U.S. Women's Cup, played well in the second half after struggling against the Canadians during the first 45 minutes.
Golebiowski, a W-League alum, has scored three goals in six matches for Australia after going without a goal in her first 38 international appearances.
Goalkeeper Melissa Barbieri made one exceptional save to earn the shutout in her international debut. She is the first player from the Australian state of Victoria to play for the Matildas since 1995.
Canada, preparing for the CONCACAF Women's Gold Cup, which will determine the region's qualifiers for next year's Women's World Cup, won Thursday in Burnaby, British Columbia, earning a 2-0 victory on a pair of second-half goals by Isabelle Morneau.